Using of Developable Surfaces as Acoustics Screens

Abstract

A significant place of modern acoustics problems is occupied by the necessity of surfaces reflections construction of the 2nd order and more complex ones. Due to the proposed systematization of reflecting surfaces on the principle of surfaces of normal to their generatrix, reflective surfaces are divided into five groups. The first group includes reflectors with beams of parallel direct normals to generatrices of developable surfaces. As reflectors, the developable surfaces are convenient to use, they are easy to create, are scattered and their transformation makes it possible to universalize the spectacle halls by changing the position of the reflecting screens and their shape, which affects the formation of zones of sound energy reception, its concentration or dispersion, and also due to the transformation it is possible to change the time of reverberation in the spectacle halls.Developable surfaces are tangent to the intersection of the two surfaces of the second order or the double method, which is the method of running two surfaces of the second order or second order curves, or two curves of the second order. On the basis of these methods, the article deals with general methods of constructing developable surfaces of the 4-8th order of 3 and 4 classes and researches the properties of the congruence of the reflected rays, and, on the example of time cases, variants of the implementation of applied problems are offered. These cases are considered as most adaptable to the mechanical solution of the problem of constructing reflectors: developable surfaces obtained by rolling plane on two curves of the second order, which lie in parallel planes, perpendicular or at an angle. Due to the well-known equation of single-valued correspondence for the creation of torso surfaces, there is an analytical description of the surfaces of reflected rays. The congruence of normals of the developable surfaces is divided into a plane of parallel lines. The two-parameter set of reflected rays is divided into flat beams of straight lines, which can be constructed in two ways: relative to the surface of normal or tangent to the generatrix of the developable surface.